Lamb Shift In Hydrogen Research Articles

Leading logarithmic contribution to the second-order lamb shift induced by the loop-after-loop diagram.

The contribution of order alpha(2)(Zalpha)(6)ln (3)(Zalpha)(-2) to the ground-state Lamb shift in hydrogen induced by the loop-after-loop diagram is evaluated analytically. An additional contribution of this order is found compared to the previous calculation by Karshenboim [Sov. Phys. JETP 76, 541 (1993)]. As a result, agreement is achieved for this correction between different numerical and analytical methods.

Effects of QED and Beyond from the Atomic Binding Energy

Atomic binding energies are calculated at utmost precision. A report on the current status of Lamb-shift predictions for hydrogenlike ions, including all quantum electrodynamical corrections to first and second order in the fine structure constant α is presented. All relevant nuclear effects are taken into account. High-precision calculations for the Lamb shift in hydrogen are presented. The hyperfine structure splitting and the g factor of a bound electron in the strong electromagnetic field of a heavy nucleus is considered. Special emphasis is also put on parity violation effects in atomic systems. For all systems possible investigations beyond precision tests of quantum electrodynamics are considered.

The Muonic Hydrogen Lamb Shift Experiment at PSI

A measurement of the 2S Lamb shift in muonic hydrogen (µ − p) is being prepared at the Paul Scherrer Institute (PSI). The goal of the experiment is to measure the energy difference �E( 2 5 P3/2 − 2 3 S1/2) by laser spectroscopy (λ ≈ 6µm) to a precision of 30 ppm and to deduce the root mean square (rms) proton charge radius with 10 −3 relative accuracy, 20 times more precise than presently known. An important prerequisite to this experiment is the availability of long-lived µp2S -atoms. A 2S- lifetime of ∼1 µs - sufficiently long to perform the laser experiment - at H2 gas pressures of 1-2 hPa was deduced from recent measurements of the collisional 2S-quenching rate. A new low-energy negative muon beam yields an order of magnitude more muon stops in a small low-density gas volume than a conventional cloud muon beam. A stack of ultra-thin carbon foils is the key element of a fast detector for keV-muons. The development of a 2 keV X-ray detector and a 3-stage laser system providing 0.5 mJ laser pulses at 6 µ mi s on the way.

Hadronic vacuum polarization contribution to the Lamb shift in muonic hydrogen

The contribution of hadronic vacuum polarization to the Lamb shift in muonic hydrogen is evaluated with the account of modern experimental data on the cross section of e+e− annihilation into hadrons. The numerical value of this contribution to the (2P-2S) shift in muonic hydrogen is equal to 10.95 µeV.

Metrology of the hydrogen and deuterium atoms: Determination of the Rydberg constant and Lamb shifts

We present a detailed description of several experiments which have been previously reported in several letters: the determination of the 1S Lamb shift in hydrogen by a comparison of the frequencies of the 1S-3S and 2S-6S or 2S-6D two-photon transitions, and the measurement of the 2S-8S/D and 2S-12D optical frequencies. Following a complete study of the lineshape of the two-photon transitions, we provide the updated values of these frequencies which have been used in the 1998 adjustment of the fundamental constants. From an analysis taking into account these results and several other precise measurements by other authors, we show that the optical frequency measurements have superseded the microwave determination of the 2S Lamb shift and we deduce optimized values for the Rydberg constant, = 109 737.315 685 50(84) cm-1 (relative uncertainty of ) and for the 1S and 2S Lamb shifts L(1S) = 8 172.840(22) MHz and L(2S-2P) = 1 057.8450(29) MHz (respectively, 8 183.970(22) MHz and 1 059.2341(29) MHz for deuterium). These are now the most accurate values available.

Coulomb corrections to elastic electron–proton scattering and the proton charge radius

Recent values of the proton charge radius derived from the Lamb shift in electronic hydrogen tend to be larger than those from electron scattering. Therefore low-momentum-transfer scattering data from different experiments have been reanalyzed with Coulomb and recoil corrections included. This was done by calculating at each scattering angle and scattering energy the corresponding correction obtained from a partial wave program which includes recoil approximately. Corrections due to magnetic scattering were also made before the rms-radius was determined by a fit which allows free normalization for each experiment. It is shown that the inclusion of Coulomb corrections in the analysis of electron scattering data lowers the χ 2 of the fit and increases the proton radius by about (0.008–0.013) fm depending on the fit strategy. A value of r p=0.880 (15) fm is obtained which is in good agreement with the one extracted from Lamb shift measurements.

Experiment to measure the Lamb shift in muonic hydrogen

The contribution of the root mean square (RMS) proton charge radius to the Lamb shift (2S–2P energy difference) in muonic hydrogen (μp) amounts to 2%. Apart from the uncertainty on this charge radius, theory predicts the Lamb shift with a precision on the ppm level. We are going to measure ΔE (2 S1/2(F=1)–2 P3/2(F=2)) in a laser resonance experiment to a precision of 30 ppm (i.e., 10% of the natural linewidth) and to deduce the RMS proton charge radius with 10−3 relative accuracy, 20 times more precise than presently known. The most important requirement for the feasibility of such an experiment, namely the availability of a sufficient amount of long lived metastable μp atoms in the 2S state, has been investigated in a recent experiment at PSI. Our analysis shows that in the order of one percent of all muons stopped in low pressure hydrogen gas form a long lived μp(2S) with a lifetime of the order of 1 μs. The technical realization of our experiment involves a new high intensity low energy muon beam, an efficient low energy muon entrance detector, a randomly triggered 3 stage laser system providing the 0.5 mJ, 7 ns laser pulses at 6.02 μm wavelength, and a combination of a xenon gas proportional scintillation chamber (GPSC) and a microstrip gas chamber (MSGC) with a CsI coated surface to detect the 2 keV X rays from theμp(2P → 1S) transition.

Accuracy of calculations involvingα3vacuum-polarization diagrams: Muonic hydrogen Lamb shift and muong−2

The contribution of the ${\ensuremath{\alpha}}^{3}$ single electron-loop vacuum-polarization diagrams to the Lamb shift of muonic hydrogen has been evaluated recently by two independent methods. One uses the exact parametric representation of the vacuum-polarization function while the other relies on the Pad\'e approximation method. The high precision of these values offers an opportunity to examine the reliability of the Monte Carlo integration as well as that of the Pad\'e method. Our examination covers both the muonic hydrogen atom and muon $g\ensuremath{-}2.$ We test them further for the cases involving two-loop vacuum polarization, where an exact analytic result is known. Our analysis justifies the result for the Lamb shift of muonic hydrogen and also resolves the long-standing discrepancy between two previous evaluations of the muon $g\ensuremath{-}2$ value.

What do we actually know about the proton radius?

This paper considers the different determinations of the proton charge radius. It demonstrates that the results from the elastic electron-proton scattering have to be assigned a higher uncertainty. A review of the hydrogen Lamb-shift measurements and the radius determination from them is also presented.PACS No.: 27.10 and 35.10B

Sixth-Order Vacuum-Polarization Contribution to the Lamb Shift of Muonic Hydrogen

The sixth-order electron-loop vacuum-polarization contribution to the $2P_{1/2} - 2S_{1/2}$ Lamb shift of the muonic hydrogen ($\mu^{-} p^+$ bound state) has been evaluated numerically. Our result is 0.007608(1) meV. This eliminates the largest uncertainty in the theoretical calculation. Combined with the proposed precision measurement of the Lamb shift it will lead to a very precise determination of the proton charge radius.

Anomalousgvalues of the electron and muon

Historically, the spin magnetic moment of the electron µ e or its gvalue g e has played a central role in modern physics, dating from its discovery in atomic optical spectroscopy and its subsequent incorporation in the Dirac theory of the electron, which predicted the value g e = 2 The experimental discovery in atomic microwave spectroscopy that g e was larger than 2 by a multiplicative factor of about 1 part in 103, g e =2.00238(10), together with the discovery of the Lamb shift in hydrogen (S=22 S 1/2 − 22 P 1/2), led to the development of modern quantum electrodynamics with its renormalization procedure. The theory enables us to calculate these effects precisely as finite radiative corrections. By now the experimental value of g e -2has been measured to about 4 ppb, and the theoretical value, which is expressed as a power series in the fine-structure constant a, has been evaluated to better than 1 ppb, assuming the value of α is known.

Nucleon polarizability contribution to the hydrogen Lamb shift and hydrogen-deuterium isotope shift

The correction to the hydrogen Lamb shift due to the proton electric and magnetic polarizabilities is expressed analytically through their static values, which are known from experiment. The numerical value of the correction to the hydrogen 1S state is −71 ± 11 ± 7 Hz. Correction to the H-D 1S–2S isotope shift due to the proton and neutron polarizabilities is estimated as 53 ± 9 ± 11 Hz.

Maximal acceleration corrections to the Lamb shift of hydrogen, deuterium and He +

The maximal acceleration corrections to the Lamb shift of one-electron atoms are calculated in a nonrelativistic approximation. They are compatible with experimental results, are in particularly good agreement with the 2 S2 P Lamb shift in hydrogen and reduce by ∼ 50% the experiment-theory discrepancy for the 2 S2 P shift in He +.

Perturbed Orbital Contribution to the Two-Loop Lamb Shift in Hydrogen

A part of the two-loop Lamb shift called the perturbed orbital term is evaluated with exact Dirac-Coulomb propagators. It is shown to be the most nonperturbative function of $Z\ensuremath{\alpha}$ yet encountered in QED, so much so that even at $Z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ the leading term in its $Z\ensuremath{\alpha}$ expansion is of the opposite sign from the complete answer. The higher order contributions are $\ensuremath{-}71(1)\phantom{\rule{0ex}{0ex}}\mathrm{kHz}$ to the ground state Lamb shift in hydrogen and $\ensuremath{-}8.9(1)$ and $\ensuremath{-}346(1)\phantom{\rule{0ex}{0ex}}\mathrm{kHz}$ to the $n\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2$ Lamb shift in hydrogen and ${\mathrm{He}}^{+}$, respectively.

Lamb-shift measurement in hydrogen by the anisotropy method

A high-precision measurement of the Lamb shift in hydrogen by theanisotropy method is presented. The result of 1057.852(15) MHz isconsistent with theory and other measurements, thereby confirming thatthe anisotropy method and its interpretation are valid at the 15 partsper million level of accuracy. For the case of He+, a discrepancyof 70(12) parts per million between theory (including two-loop bindingcorrections) and experiment remains to be resolved.PACS Nos. 3130J, 3220D

High precision tests of QED and physics beyondthe standard model

We study the four most significant high precision observables of QED ---the anomalous electron and muon magnetic moments, the hydrogen Lamb shift and muonium hyperfine splitting--- in the context of SU(2) x U(1) gauge-invariant effective Lagrangians. The agreement between the theoretical predictions for these observables and the experimental data places bounds on the lowest dimension operators of the effective Lagrangians. We also place bounds on such effective operators using other experimental data. Comparison of the tow types of bounds allows us to discuss the potential of each one of the four high precision observables in the search for physics beyond the Standard Model. We find that the anomalous electron and muon magnetic moments are sensitive to new physics while the hydrogen Lamb shift and muonium hyperfine splitting are not.

Lamb-shift measurement in hydrogen by the anisotropy method

A high-precision measurement of the Lamb shift in hydrogen by theanisotropy method is presented. The result of 1057.852(15) MHz isconsistent with theory and other measurements, thereby confirming thatthe anisotropy method and its interpretation are valid at the 15 partsper million level of accuracy. For the case of He+, a discrepancyof 70(12) parts per million between theory (including two-loop bindingcorrections) and experiment remains to be resolved.PACS Nos. 3130J, 3220D

Quantum electrodynamics of weakly bound systems

An overview of quantum electrodynamic effects in two-body systems is presented. Recent advances in the calculation of the hydrogen Lamb shift, muonium hyperfine structure, and positronium energy levels are described in detail. The comparison of experimental results to current theoretical predictions gives agreement in most cases. However, a few significant discrepancies remain, which indicates the necessity for further refined calculations and measurements.

What do we actually know about the proton radius?

The work is devoted to a consideration of the different determinations of the proton charge radius. It is demonstrated that the results from the elastic electron-proton scattering have to be of a higher uncertainty. A review of the hydrogen Lamb shift measurements and the radius determination from them is also presented.

Lamb shift in a light-front Hamiltonian approach

Light-front Hamiltonian methods are being developed to attack bound-state problems in QCD. In this paper we advance the state of the art for these methods by computing the well-known Lamb shift in hydrogen starting from first principles of QED. There are obvious but significant qualitative differences between QED and QCD. In this paper, we discuss the similarities that may survive in a non-perturbative QCD calculation in the context of a precision non-perturbative QED calculation. Central to the discussion are how a constituent picture arises in a gauge field theory, how bound-state energy scales emerge to guide the renormalization procedure, and how rotational invariance emerges in a light-front calculation.